Hi,
Thanks for your interest in Microsoft academic search.
I did try your URL http://academic.research.microsoft.com/json.svc/search?AppId=myAppId&PublicationID=4242890&ResultObjects=Publication&ReferenceType=Reference&StartIdx=1&EndIdx=2&OrderBy=Year
it worked as expected. It gets reference data for all the 16 publications available. Yes website and API share the same database and the data should be identical.
Just make a small change in your requesting URL EndIdx. set the value of EndIdx to 16 and you should be able to see publications related data as shown in the below screenshot.

Please revert back if you have any further queries.
Prapthi